{"id":263,"date":"2026-01-30T23:00:10","date_gmt":"2026-01-30T23:00:10","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/chapter\/linear-functions-get-stronger-key-precalculus-practice-page-answer-keys\/"},"modified":"2026-08-07T16:44:02","modified_gmt":"2026-08-07T16:44:02","slug":"linear-functions-get-stronger-key-precalculus-practice-page-answer-keys","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/chapter\/linear-functions-get-stronger-key-precalculus-practice-page-answer-keys\/","title":{"raw":"Linear Functions: Get Stronger Key -- Precalculus Practice Page Answer Keys","rendered":"Linear Functions: Get Stronger Key — Precalculus Practice Page Answer Keys"},"content":{"raw":"

Graphs of Linear Functions Solutions<\/h2>\r\n1. The point of intersection is (a,a). This is because for the horizontal line, all of the y coordinates are a and for the vertical line, all of the x coordinates are a. The point of intersection will have these two characteristics.\r\n\r\n2. First, find the slope of the linear function. Then take the negative reciprocal of the slope; this is the slope of the perpendicular line. Substitute the slope of the perpendicular line and the coordinate of the given point into the equation y=mx+b and solve for b. Then write the equation of the line in the form y=mx+b by substituting in m and b.\r\n\r\n3. (-2, 0) ; (0, 4)\r\n\r\n4. (8, 0) ; (0, 28)\r\n\r\n5. g(x)=3x-3\r\n\r\n6. p(t)=-1\/3t+2\r\n\r\n7. \"\"\r\n\r\n8. \"\"\r\n\r\n9. \"\"\r\n\r\n10. \"\"\r\n\r\n11. y=3\r\n\r\n12. x=-3\r\n

Linear Functions Solutions<\/h2>\r\n1. 3 miles per hour\r\n\r\n2. d(t)=100-10t\r\n\r\n3. Increasing.\r\n\r\n4. Decreasing.\r\n\r\n5. 3\r\n\r\n6. y=2x+3\r\n\r\n7. y=4\/5x+4\r\n\r\n8. y=2\/3x+1\r\n\r\n9. Linear, g(x)=-3x+5\r\n\r\n10. Linear, f(x)=5x-5\r\n\r\n11. 0\r\n\r\n12. y=2x-2\r\n\r\n13. Parallel\r\n\r\n14. Parallel\r\n\r\n15. y=-1\/5x+21\r\n\r\n16. $45 per session\r\n\r\n17. The rate of change is 0.1 which represents 10 cents ($0.10) per minute talked. The initial value is 24 which represents a flat monthly fee.\r\n\r\n18. c\r\n

Modeling with Linear Functions Solutions<\/h2>\r\n1. To determine the initial value, find the output when the input is equal to zero.\r\n\r\n2. Look for words like \"per\" or \"for every\" or \"for each\" since slope describes how fast the quantity changes.\r\n\r\n3. 2,300\r\n\r\n4. Between 2019 and 2020\r\n\r\n5. C(t)=12,025-205t\r\n\r\n6. (58.7,0): In roughly 59 years, the number of people inflicted with the common cold would be 0. (0,12,025): Initially there were 12,025 people afflicted by the common cold.\r\n\r\n7. y=30t-300\r\n\r\n8. In 1980 the profit would be -$300.\r\n\r\n9. (10,0) In 1990, the profit earned zero profit.\r\n\r\n10. Every year the profit increases by $30.\r\n\r\n11. a. 696 people b. 4 years c. 174 people per year d. 305 people e. P(t)=305+174t f. 2219 people\r\n\r\n12. a. R(t)=16-2.1t b. 5.5 billion cubic feet c. During the year 2017\r\n\r\n13. More than 133 minutes\r\n

Fitting Linear Models to Data Solutions<\/h2>\r\n1. 61.966 years\r\n\r\n2. No\r\n\r\n3. No\r\n\r\n4. D\r\n\r\n5. C\r\n\r\n6. A\r\n\r\n7. B\r\n\r\n8. \"\"\r\n\r\n9. \"\"\r\n\r\n10. Yes, trend appears linear because r=0.985 and will exceed 12,000 near midyear, 2016, 24.6 years since 1992.\r\n\r\n11. y=1.640x+13.800, r=0.987\r\n\r\n12. y=-0.962x+26.86, r=-0.965\r\n\r\n13. Use linear regression... [needs verification against doc25 #34]\r\n\r\n14. Predict when profit dips below $25,000","rendered":"

Graphs of Linear Functions Solutions<\/h2>\n

1. The point of intersection is (a,a). This is because for the horizontal line, all of the y coordinates are a and for the vertical line, all of the x coordinates are a. The point of intersection will have these two characteristics.<\/p>\n

2. First, find the slope of the linear function. Then take the negative reciprocal of the slope; this is the slope of the perpendicular line. Substitute the slope of the perpendicular line and the coordinate of the given point into the equation y=mx+b and solve for b. Then write the equation of the line in the form y=mx+b by substituting in m and b.<\/p>\n

3. (-2, 0) ; (0, 4)<\/p>\n

4. (8, 0) ; (0, 28)<\/p>\n

5. g(x)=3x-3<\/p>\n

6. p(t)=-1\/3t+2<\/p>\n

7. \"\"<\/p>\n

8. \"\"<\/p>\n

9. \"\"<\/p>\n

10. \"\"<\/p>\n

11. y=3<\/p>\n

12. x=-3<\/p>\n

Linear Functions Solutions<\/h2>\n

1. 3 miles per hour<\/p>\n

2. d(t)=100-10t<\/p>\n

3. Increasing.<\/p>\n

4. Decreasing.<\/p>\n

5. 3<\/p>\n

6. y=2x+3<\/p>\n

7. y=4\/5x+4<\/p>\n

8. y=2\/3x+1<\/p>\n

9. Linear, g(x)=-3x+5<\/p>\n

10. Linear, f(x)=5x-5<\/p>\n

11. 0<\/p>\n

12. y=2x-2<\/p>\n

13. Parallel<\/p>\n

14. Parallel<\/p>\n

15. y=-1\/5x+21<\/p>\n

16. $45 per session<\/p>\n

17. The rate of change is 0.1 which represents 10 cents ($0.10) per minute talked. The initial value is 24 which represents a flat monthly fee.<\/p>\n

18. c<\/p>\n

Modeling with Linear Functions Solutions<\/h2>\n

1. To determine the initial value, find the output when the input is equal to zero.<\/p>\n

2. Look for words like “per” or “for every” or “for each” since slope describes how fast the quantity changes.<\/p>\n

3. 2,300<\/p>\n

4. Between 2019 and 2020<\/p>\n

5. C(t)=12,025-205t<\/p>\n

6. (58.7,0): In roughly 59 years, the number of people inflicted with the common cold would be 0. (0,12,025): Initially there were 12,025 people afflicted by the common cold.<\/p>\n

7. y=30t-300<\/p>\n

8. In 1980 the profit would be -$300.<\/p>\n

9. (10,0) In 1990, the profit earned zero profit.<\/p>\n

10. Every year the profit increases by $30.<\/p>\n

11. a. 696 people b. 4 years c. 174 people per year d. 305 people e. P(t)=305+174t f. 2219 people<\/p>\n

12. a. R(t)=16-2.1t b. 5.5 billion cubic feet c. During the year 2017<\/p>\n

13. More than 133 minutes<\/p>\n

Fitting Linear Models to Data Solutions<\/h2>\n

1. 61.966 years<\/p>\n

2. No<\/p>\n

3. No<\/p>\n

4. D<\/p>\n

5. C<\/p>\n

6. A<\/p>\n

7. B<\/p>\n

8. \"\"<\/p>\n

9. \"\"<\/p>\n

10. Yes, trend appears linear because r=0.985 and will exceed 12,000 near midyear, 2016, 24.6 years since 1992.<\/p>\n

11. y=1.640x+13.800, r=0.987<\/p>\n

12. y=-0.962x+26.86, r=-0.965<\/p>\n

13. Use linear regression… [needs verification against doc25 #34]<\/p>\n

14. Predict when profit dips below $25,000<\/p>\n","protected":false},"author":13,"menu_order":3,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":224,"module-header":"- Select Header -","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/263"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/users\/13"}],"version-history":[{"count":6,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/263\/revisions"}],"predecessor-version":[{"id":389,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/263\/revisions\/389"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/parts\/224"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/263\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/media?parent=263"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapter-type?post=263"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/contributor?post=263"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/license?post=263"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}